Development of a high-order level set method: Compact Conservative Level Set (CCLS)

•Application of oscillatory high-order advection schemes to transport CLS function are investigated.•Spurious numerical oscillations occurred during advection of CLS are resolved by re-initialization.•A novel CCD scheme for solving re-initialization equation is developed.•Mass conservation error of CLS method is improved to less than 1E−12 for different test cases. In this paper a Compact Conservative Level Set (CCLS) method has been developed to improve the accuracy and robustness of Level Set (LS) approach in simulation of incompressible two-phase flows. Since mass conservation error is known as the evident weakness of LS approach, the main aim of this research is to introduce a novel method with an excellent mass conservation property while keeping the simplicity of the approach. Here, the hyperbolic tangent function; used as LS function; is conservatively transported through a High-Order Compact (HOC) finite difference scheme. In order to retain thickness of the coated interface while retrieving the hyperbolic tangent profile, a conservative re-initialization is adopted by introducing a novel Combined Compact Difference (CCD) method. Normals are computed from the distance function, where a fast marching method; an efficient re-distancing method; is applied to re-construct signed distance function from the hyperbolic tangent function. The developed method is employed in a wide range of test cases and its noticeable mass conservation property is revealed even for complex cases, as well as its accuracy and stability in large courant numbers, long time simulation, coarse mesh and even simulations without re-initialization.